A Class of Statistical and σ-Conservative Matrices

In [5] and [10], statistical-conservative and σ-conservative matrices were characterized. In this note we have determined a class of statistical and σ-conservative matrices studying some inequalities which are analogous to Knopp's Core Theorem.     

Elemental‐Sulfur‐Mediated Facile Synthesis of a Covalent Triazine Framework for High‐Performance Lithium–Sulfur Batteries

A covalent triazine framework (CTF) with embedded polymeric sulfur and a high sulfur content of 62 wt % was synthesized under catalyst‐ and solvent‐free reaction conditions from 1,4‐dicyanobenzene and elemental sulfur. Our synthetic approach introduces a new way of preparing CTFs under environmentally benign conditions by the direct utilization of elemental sulfur. The homogeneous sulfur distribution is due to the in situ formation of the framework structure, and chemical sulfur impregnation within the micropores of CTF effectively suppresses the dissolution of polysulfides into the electrolyte. Furthermore, the triazine framework facilitates electron and ion transport, which leads to a high‐performance lithium–sulfur battery.     

A new approach to liquid penetrant inspection: radiolabeled QDots

Penetrant technique is a sensitive non-destructive testing (NDT) method for detecting and locating the presence of cracks in sample surface. Today, NDT is used in a wide range of industries including aerospace, biotechnology, defence, marine, oil–gas and energy plants. This work focuses on potential use of radiolabeled ZnS coated CdTe quantum dots (QDots) as a penetrant for liquid penetrant testing. The synthesized QDots as a precursor were tested for surface defects detection in welded joints. The experimental results show the highest activities were found in defects on the sample surface. These finding are consistent with the sample NDT inspection test report.     

Flexibility of Schubert classes

In this note, we discuss the flexibility of Schubert classes in homogeneous varieties. We give several constructions for representing multiples of a Schubert class by irreducible subvarieties. We sharpen [22, Theorem 3.1] by proving that every positive multiple of an obstructed class in a cominuscule homogeneous variety can be represented by an irreducible subvariety.     

Hilbert Scheme of a Pair of Codimension Two Linear Subspaces

We study the component H _n of the Hilbert scheme whose general point parameterizes a pair of codimension two linear subspaces in ? ⁿ for n ≥ 3. We show that H _n is smooth and isomorphic to the blow-up of the symmetric square of 𝔾(n ? 2, n) along the diagonal. Further H _n intersects only one other component in the full Hilbert scheme, transversely. We determine the stable base locus decomposition of its effective cone and give modular interpretations of the corresponding models, hence conclude that H _n is a Mori dream space.     

Variation of parameters formulae with initial time difference for linear integrodifferential equations

This article investigates the relationship between an unperturbed integrodifferential system and a perturbed integrodifferential system that have different initial positions and an initial time difference (ITD). Variation of parameter techniques are employed to obtain integral formulae and to define Lyapunov-like functions.     

A Littlewood–Richardson rule for two-step flag varieties

This paper studies the geometry of one-parameter specializations of subvarieties of Grassmannians and two-step flag varieties. As a consequence, we obtain a positive, geometric rule for expressing the structure constants of the cohomology of two-step flag varieties in terms of their Schubert basis. A corollary is a positive, geometric rule for computing the structure constants of the small quantum cohomology of Grassmannians. We also obtain a positive, geometric rule for computing the classes of subvarieties of Grassmannians that arise as the projection of the intersection of two Schubert varieties in a partial flag variety. These rules have numerous applications to geometry, representation theory and the theory of symmetric functions. Mathematics Subject Classification (2000)  Primary 14M15, 14N35, 32M10     

Normal bundles of rational curves in projective space

Mathematische Zeitschrift - Let $$b_{\bullet }$$ be a sequence of integers $$1 < b_1 \le b_2 \le \cdots \le b_{n-1}$$ . Let $${\text {M}}_e(b_{\bullet })$$ be the space parameterizing...     

Gromov-Witten invariants of jumping curves

Given a vector bundle on a smooth projective variety , we can define subschemes of the Kontsevich moduli space of genus-zero stable maps parameterizing maps such that the Grothendieck decomposition of has a specified splitting type. In this paper, using a ``compactification' of this locus, we define Gromov-Witten invariants of jumping curves associated to the bundle . We compute these invariants for the tautological bundle of Grassmannians and the Horrocks-Mumford bundle on . Our construction is a generalization of jumping lines for vector bundles on . Since for the tautological bundle of the Grassmannians the invariants are enumerative, we resolve the classical problem of computing the characteristic numbers of unbalanced scrolls.